XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,299,330

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/17/2017, 3:06:43 PM Β· Difficulty 10.9394 Β· 4,533,992 confirmations

2CC
Cunningham Chain of the Second Kind

A sequence where each prime is double the previous prime minus one.

Block Header
Block Hash
b3ed13a0738037bf70229a3d423d695dc03d438ad299aaeecd10906aa1435e5b
View on Chainz β†—

Height

#2,299,330

Difficulty

10.939430

Transactions

2

Size

425 B

Version

2

Bits

0af07e74

Nonce

1,124,830,400

Timestamp

9/17/2017, 3:06:43 PM

Confirmations

4,533,992

Mined by

⛏️ P2SHAYuBSGT5FGX9K94Uyv1F7drjVBP5YGuHyc

Merkle Root

08c99a369ddd683404a0e3d5ee6e239b3e5826decafde667003a2b188bc1a0fc
Transactions (2)
Coinbase23a0111db7a345…18a1687bd72121
1 in β†’ 1 out8.3500 XPM109 B
AYuBSGT5…P5YGuHyc
45b85c45894875…3700a6d6d7c33e
1 in β†’ 2 out1979.9900 XPM227 B
AYC8sryY…X6t9WkCfAU7xkW52…RMPvkSaU
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

2.641 Γ— 10⁹³(94-digit number)
26413924208740247084…94337205434606412161
Discovered Prime Numbers
p_k = 2^k Γ— origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

1
origin + 1
2.641 Γ— 10⁹³(94-digit number)
26413924208740247084…94337205434606412161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.282 Γ— 10⁹³(94-digit number)
52827848417480494168…88674410869212824321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.056 Γ— 10⁹⁴(95-digit number)
10565569683496098833…77348821738425648641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.113 Γ— 10⁹⁴(95-digit number)
21131139366992197667…54697643476851297281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.226 Γ— 10⁹⁴(95-digit number)
42262278733984395335…09395286953702594561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.452 Γ— 10⁹⁴(95-digit number)
84524557467968790670…18790573907405189121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.690 Γ— 10⁹⁡(96-digit number)
16904911493593758134…37581147814810378241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.380 Γ— 10⁹⁡(96-digit number)
33809822987187516268…75162295629620756481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.761 Γ— 10⁹⁡(96-digit number)
67619645974375032536…50324591259241512961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.352 Γ— 10⁹⁢(97-digit number)
13523929194875006507…00649182518483025921
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Cunningham Chain of the Second Kind. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜…β˜†β˜†β˜†
Rarity
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,910,769 XPMΒ·at block #6,833,321 Β· updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.
Privacy PolicyΒ·
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

Cookie Preferences

We use cookies to enhance your experience. Some are essential for the site to function, while others help us understand how you use the site.

Β·Privacy Policy